The following is content drawn from 30 Philosophers but adds Pythagoras as an example to the discussion. Read chapter 22 for a more in depth exploration.
Introduction
Pythagoras is a fascinating case study in both sound and flawed thinking. On one hand, his mathematical insights—especially in geometry and harmonics—were grounded in observation and logical reasoning. On the other hand, his mystical interpretations and rigid numerical dogmatism led him badly astray. For our purposes here, Pythagoras is especially useful because he shows how many people approach truth: not with perfect consistency, but through a pragmatic lens.
He also reminds us that authority is often topic specific. Pythagoras was a good authority on math, but not on everything he believed. That tension makes him an ideal figure for exploring pragmatism, because it shows how a person can contribute lasting insight in one area while remaining deeply mistaken in another.
Pragmatism
At its core, pragmatism values practical application over strict intellectual purity. William James, a key figure in shaping this tradition, famously wrote in his 1907 book Pragmatism: A New Name for Some Old Ways of Thinking:
The pragmatic method is primarily a method of settling metaphysical disputes…and disputes over such notions are unending. … What difference would it practically make to anyone if this notion rather than that notion were true? If no practical difference whatever can be traced, then the alternatives mean practically the same thing, and all dispute is idle.
This tradition emerged in the United States in the late 19th century and argues that the value of an idea is tied to its practical consequences. In other words, if an idea works in practice, it is often treated as having merit. Nearly everyone is pragmatic to some degree, whether they realize it or not. Most of us assign different levels of practical value to beliefs and use them accordingly in everyday life.
But pragmatism comes in different forms. Some people try to follow only what is testable. Most balance evidence with personal belief. Others dismiss good evidence when it gets in the way. That is why Pythagoras is such a useful example. He helps us explore not just pragmatism in general, but the important differences between empirical pragmatists, rational pragmatists, and irrational pragmatists.
Pragmatism and Pythagoras
Pythagoras exemplifies the three types of pragmatism introduced in chapter 22 of 30 Philosophers: empirical, rational, and irrational pragmatism.
Pythagoras as a Rational Pragmatist
Pythagoras’ belief system often overpowered his science, yet some of his observations stood the test of time. That makes him a strong example of a rational pragmatist—someone who accepts empirical and rational truths, but also makes room for personal beliefs, sometimes at the cost of reason. Unfortunately for his reputation, many of those personal beliefs were very wrong.
Most people fall into this category. They embrace empirical and rational ideas, but also hold spiritual, religious, or deeply personal convictions. Rational pragmatists can still make meaningful contributions while carrying beliefs that do not survive scrutiny. Pythagoras is a perfect example: brilliant on math and harmonics, yet drawn into mystical claims about numbers as divine forces governing reality.
He is also a good example of topic-specific authority. Pythagoras was a good authority on math, but not on everything he believed. That is true of most authorities, ancient and modern. A person may be insightful in one area and badly mistaken in another. Good authority is usually narrow, not universal.
The Empirical Pragmatist: Seeking What Can Be Tested
In contrast, an empirical pragmatist rejects irrational beliefs and follows empirical and rational truths alone. This mindset aligns closely with the modern scientific method: trust what can be tested, examined, and verified. An empirical pragmatist does not mix in unsupported belief systems simply because they feel meaningful or comforting.
If Pythagoras had been an empirical pragmatist, he would have let go of his mystical numerology when the evidence failed to support it. Instead, he held onto the supernatural significance of numbers despite the lack of good evidence.
The Irrational Pragmatist: Dismissing Good Evidence
Finally, we can contrast both empirical and rational pragmatists with the irrational pragmatist. This is the person who does not merely hold unproven beliefs, but dismisses good evidence when it gets in the way. That is the key dividing line.
A rational pragmatist may blend evidence with personal belief, but still respects good evidence. An irrational pragmatist does not. Instead, they cling to disproven, unsupported, or unfalsifiable ideas because those ideas feel useful, comforting, or identity-affirming. Phrases like “everyone has their own truth” or “truth isn’t truth” capture this posture well. This is not simple humility about what we do not know. It is a refusal to let good evidence place limits on belief.
Whereas Pythagoras at least engaged in observation, reasoning, and mathematical discovery, the irrational pragmatist dismisses the need for evidence whenever it threatens a preferred conclusion. And that is why those who dismiss good evidence are rarely good authorities on much of anything.
Pythagoras and the Nature of Intellectual Progress
The mathematical insights associated with Pythagoras, especially in geometry and harmonics, were rooted in observation and logical reasoning. Yet he also helped father numerological mysticism and other flawed ideas. That tension matters because it reveals something important about intellectual progress: before an idea can be tested, someone has to think it up.
Some ideas survive the test of time. Others collapse under it.
That is part of the human story. Rational pragmatism is so common because most people do not live by evidence alone. They mix reason with hope, tradition, loyalty, and private conviction. That does not make all beliefs equal, but it does help explain how human thought actually works. Even flawed thinkers can move knowledge forward. The challenge is separating the lasting insight from the illusion.
Final Thoughts
Pythagoras’ legacy is a reminder of both the power and the danger of human reasoning. His blend of observation, logic, and mystical belief makes him a clear example of rational pragmatism in action.
Understanding the three types of pragmatism—empirical, rational, and irrational—helps us better understand not just Pythagoras, but ourselves. Some people try to follow only what is testable. Most balance evidence with personal belief. And some dismiss good evidence altogether. That last group is rarely a good authority on much of anything.
The broader lesson is simple: choose your authorities by subject matter. A person may offer real insight in one area and poor judgment in another. Even flawed ideas can spark progress, but our task is to distinguish insight from illusion.
